https://doi.org/10.1140/epjp/i2018-11953-8
Regular Article
A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives
1
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
2
Department of Electrical Engineering, Mehran University of Engineering and Technology, Jamshoro, Pakistan
* e-mail: kashif.abro@faculty.muet.edu.pk
Received:
24
October
2017
Accepted:
22
February
2018
Published online:
19
March
2018
This research article is analyzed for the comparative study of RL and RC electrical circuits by employing newly presented Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. The governing ordinary differential equations of RL and RC electrical circuits have been fractionalized in terms of fractional operators in the range of 
and 
. The analytic solutions of fractional differential equations for RL and RC electrical circuits have been solved by using the Laplace transform with its inversions. General solutions have been investigated for periodic and exponential sources by implementing the Atangana-Baleanu and Caputo-Fabrizio fractional operators separately. The investigated solutions have been expressed in terms of simple elementary functions with convolution product. On the basis of newly fractional derivatives with and without singular kernel, the voltage and current have interesting behavior with several similarities and differences for the periodic and exponential sources.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
